## Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green |

### Inni boken

Side 5

A

A

**single**capital letter , as A , or B , in reference to a Diagram , denotes the point A , or the point B.**Two**capital letters ...**two**letters indicate opposite**angles**, they denote a square , a rectangle , a parallelogram , or a polygon ... Side 7

Indirect Demonstration is when

Indirect Demonstration is when

**all other**cases , or conditions , except the**one**in question , are proved not to be ... The Supplement of**an**'**angle**( supplementum , a filling up ) , is what is wanted to make**an angle equal to two**right ... Side 8

Here in the premisses

Here in the premisses

**two**things are laid down , or granted to be true : as , — " things**equal**to the same thing are**equal**to**each other**, " — this is**one**truth ; “ the line AC**equals**the line AB , and the line BC also**equals**the same ... Side 9

5 But the Principle of Geometrical Reasoning is , that from

5 But the Principle of Geometrical Reasoning is , that from

**two**propositions established or received as true , a third ... the**other two**things are compared : we sayAll the triangle is in the circle ,**All**the square is in the triangle ... Side 10

7 , bk . i . , the

7 , bk . i . , the

**angle**BDC is proved to be , first ,**equal**to the**angle**BCD , and next , greater than the same**angle**... according to the varietie of their sides and**Angles**: and compareth them**all**with Triangles , and also together ...### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

ABCD added angle equal apply assumed Axioms base base BC bisected centre circle circumference coincide common Conc construct contained definition demonstration describe diagonal diameter distance divided draw drawn equal Euclid extremity fall feet figure four Geometry given given line given point given st greater half height impossible inches inference join length less line BC measure meet miles named opposite parallel parallelogram perpendicular plane principle produced PROP proposition proved Quæs reasoning rectangle rectilineal representative right angles scale sides square straight line suppose surface thing third triangle true truth Wherefore whole Нур

### Populære avsnitt

Side 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Side 17 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 17 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.

Side 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.

Side 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 16 - LET it be granted that a straight line may be drawn from any one point to any other point.

Side 54 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 21 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.

Side 22 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.

Side 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.